Tuesday, April 25, 2017 Individual Contest FORM A. Do Not Open This Booklet Until Instructed To Do So By The Proctor

Transcription

1 Tuesday, April 25, 2017 Individual Contest FORM A Do Not Open This ooklet Until Instructed To Do So y The Proctor

2 This page was intended to be left blank (but now it isn t).

3 1. One hundred people are standing equally spaced around a circle and are numbered 1, 2, 3,, 99, 100 in order. hat is the number of the person standing directly across from person number 88? A C. 38 D. 32 E. 24 F A city wishes to plant 100 trees in a long row and surround them with hexagonal paving slabs according to the pattern shown below. One tree requires 6 slabs, while 4 trees require 18 slabs. How many slabs are needed for 100 trees? A C. 600 D. 338 E. 450 F. 540 Figure for #2 Figure for #3 3. You are making towers with blocks that come in two colors: black and white. Shown above are the four different towers that can be made that are two blocks high. How many different possible towers are four blocks high? A C. 32 D. 10 E. 6 F Suppose that each girl in a math class has 6 more female classmates than male classmates, whereas each boy in the class has twice as many female classmates as male classmates. How many girls are there in the math class? A C. 12 D. 16 E. 9 F A painter has finished painting! of a room by 2:00 pm and " of the same room by 2:30 pm. At this " # rate, at what time in the afternoon does she finish painting the room? A. 3:30. 4:30 C. 5:30 D. 3:00 E. 5:00 F. 4:00 6. A math contest has 20 questions. Each correct answer is worth 3 points and each question left blank is worth 1 point. Incorrect answers are worth 0 points. hat is the largest number of questions someone could leave blank and score exactly 38 points? A C. 11 D. 6 E. 8 F Suppose that on the planet Zoltar, the standard unit for measuring length is the fing. There is a larger unit of length called the hand, with the following relationship: 1 hand = 5 fings. A Zoltarian has a small flower bed that covers 100 square hands. hat is this area in square fings? A. 2, ,500 C. 250 D. 500 E. 224 F. 20

4 8. In the figure below left, ACDE is a regular pentagram. Find the measure of angle CAD. A C. 40 D. 54 E. 24 F. 18 Figure for #8 Figure for #9 Figure for #10 9. Rectangle ACD (shown above) is partitioned into seven congruent rectangles. The area of rectangle ACD is 84 square centimeters. hat is the perimeter in centimeters of one of the small rectangles? A C. 9 D. 19 E. 12 F Six pipes, each with a radius 1 foot, are stacked as shown in the figure above right. Find the height of the pile (to the nearest tenth of a foot). A C. 3.1 D. 6.0 E. 2.8 F hat is the last digit of 2017!+,-? A C. 9 D. 2 E. 7 F Four students throw their coats on a counter. Their teacher randomly chooses a coat for each student. How many different ways can the coats be distributed so that no one receives the correct coat? A C. 10 D. 23 E. 9 F There are 100 second-graders enrolled at Euclid Elementary, and 80% of them are girls. Half way through the school year, the principal decides promote some of the girls (and none of the boys) to third grade. After she does this, only 75% of the second graders will be girls. How many girls will be promoted to third grade? A C. 10 D. 6 E. 12 F A full radiator has 60% anti-freeze and 40% water. The owner wishes to raise the concentration to 90% anti-freeze. hat fraction of the liquid in the radiator should be drained and replaced with pure anti-freeze? A.,!. ". C.. 0 D. #. E.! " F. " #

5 15. innie-the-pooh and Piglet set out to visit each other. They leave their houses at the same time and walk along the same road. ut it is quite foggy, so they pass one another without noticing. One minute after the meeting, innie-the-pooh is at Piglet s house, and 4 minutes after the meeting Piglet is at innie-the-pooh s. How many minutes did it take innie-the-pooh to walk from his house to Piglet s? A C. 4.5 D. 3.5 E. 5 F Noah calculated that if he averages 10 miles per hour, he will finish the bike trail at 1 PM. If he bikes 15 miles per hour, he will finish at 11 AM. How fast must he bike (in miles per hour) in order to finish at noon? A C. 12 D. 14 E. 13 F Three rugs have a combined area of 200 square meters. y overlapping the rugs to cover a floor area of 140 square meters, the area which is covered by exactly two layers of rug is 24 square meters. How many square meters of floor is covered by three layers of rug? A C. 24 D. 18 E. 12 F A cube of cheese with edge length n centimeters is dipped into red wax. Then the cube gets diced into 1 cm cubes. Some of these cubes have no wax, some have wax on just one face, some have wax on two faces, and some have wax on three faces. You count and notice that the number of cubes with no wax on them is the same as the number of cubes with wax on exactly one face. hat is the edge length n in centimeters of the original cube of cheese? A C. 8 D. 4 E. 5 F Fred and Ted are playing a game with two six-sided dice. The dice are unusual: rather than bearing a number, each face is painted either red or blue. The two take turns throwing the dice. Fred wins if the two top faces are the same color, and Ted wins if they re different. Their chances of winning are equal. The first die has 5 red faces and 1 blue face. How many faces are red on the second die? A C. 4 D. 3 E. 5 F The expression ERASE = EAR represents a true number fact, where each letter stands for a different base-ten digit. E is not 0. Find the value of S. A C. 6 D. 5 E. 2 F. 8